Eigenvalues of Killing Tensors and Separable Webs on Riemannian and Pseudo-Riemannian Manifolds
Given a $n$-dimensional Riemannian manifold of arbitrary signature, we illustrate an algebraic method for constructing the coordinate webs separating the geodesic Hamilton-Jacobi equation by means of the eigenvalues of $m leq n$ Killing two-tensors. Moreover, from the analysis of the eigenvalues, in...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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National Academy of Science of Ukraine
2007-02-01
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Subjects: | |
| Online Access: | http://www.emis.de/journals/SIGMA/2007/021/ |
| _version_ | 1818212998384189440 |
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| author | Giovanni Rastelli Claudia Chanu |
| author_facet | Giovanni Rastelli Claudia Chanu |
| author_sort | Giovanni Rastelli |
| collection | DOAJ |
| description | Given a $n$-dimensional Riemannian manifold of arbitrary signature, we illustrate an algebraic method for constructing the coordinate webs separating the geodesic Hamilton-Jacobi equation by means of the eigenvalues of $m leq n$ Killing two-tensors. Moreover, from the analysis of the eigenvalues, information about the possible symmetries of the web foliations arises. Three cases are examined: the orthogonal separation, the general separation, including non-orthogonal and isotropic coordinates, and the conformal separation, where Killing tensors are replaced by conformal Killing tensors. The method is illustrated by several examples and an application to the L-systems is provided. |
| first_indexed | 2024-12-12T05:57:18Z |
| format | Article |
| id | doaj.art-4e0917bb17754b759677135425dadf74 |
| institution | Directory Open Access Journal |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2024-12-12T05:57:18Z |
| publishDate | 2007-02-01 |
| publisher | National Academy of Science of Ukraine |
| record_format | Article |
| series | Symmetry, Integrability and Geometry: Methods and Applications |
| spelling | doaj.art-4e0917bb17754b759677135425dadf742022-12-22T00:35:31ZengNational Academy of Science of UkraineSymmetry, Integrability and Geometry: Methods and Applications1815-06592007-02-013021Eigenvalues of Killing Tensors and Separable Webs on Riemannian and Pseudo-Riemannian ManifoldsGiovanni RastelliClaudia ChanuGiven a $n$-dimensional Riemannian manifold of arbitrary signature, we illustrate an algebraic method for constructing the coordinate webs separating the geodesic Hamilton-Jacobi equation by means of the eigenvalues of $m leq n$ Killing two-tensors. Moreover, from the analysis of the eigenvalues, information about the possible symmetries of the web foliations arises. Three cases are examined: the orthogonal separation, the general separation, including non-orthogonal and isotropic coordinates, and the conformal separation, where Killing tensors are replaced by conformal Killing tensors. The method is illustrated by several examples and an application to the L-systems is provided.http://www.emis.de/journals/SIGMA/2007/021/variable separationHamilton-Jacobi equationKilling tensors(pseudo-)Riemannian manifolds |
| spellingShingle | Giovanni Rastelli Claudia Chanu Eigenvalues of Killing Tensors and Separable Webs on Riemannian and Pseudo-Riemannian Manifolds Symmetry, Integrability and Geometry: Methods and Applications variable separation Hamilton-Jacobi equation Killing tensors (pseudo-)Riemannian manifolds |
| title | Eigenvalues of Killing Tensors and Separable Webs on Riemannian and Pseudo-Riemannian Manifolds |
| title_full | Eigenvalues of Killing Tensors and Separable Webs on Riemannian and Pseudo-Riemannian Manifolds |
| title_fullStr | Eigenvalues of Killing Tensors and Separable Webs on Riemannian and Pseudo-Riemannian Manifolds |
| title_full_unstemmed | Eigenvalues of Killing Tensors and Separable Webs on Riemannian and Pseudo-Riemannian Manifolds |
| title_short | Eigenvalues of Killing Tensors and Separable Webs on Riemannian and Pseudo-Riemannian Manifolds |
| title_sort | eigenvalues of killing tensors and separable webs on riemannian and pseudo riemannian manifolds |
| topic | variable separation Hamilton-Jacobi equation Killing tensors (pseudo-)Riemannian manifolds |
| url | http://www.emis.de/journals/SIGMA/2007/021/ |
| work_keys_str_mv | AT giovannirastelli eigenvaluesofkillingtensorsandseparablewebsonriemannianandpseudoriemannianmanifolds AT claudiachanu eigenvaluesofkillingtensorsandseparablewebsonriemannianandpseudoriemannianmanifolds |